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Internalizing equality in Boolean algebras

Fearnley-Sander, D. and Stokes, T. (2000) Internalizing equality in Boolean algebras. Algebra Universalis, 43 (2-3). pp. 187-196.

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We show that equality may be internalized in Boolean algebras, in a number of possible ways, as a binary operation satisfying reflexivity and replacement properties. The variety of equality Boolean rings is shown to be equivalent to the variety of modal rings (Boolean rings endowed with a generalised interior operator and important in modal logic). Varying the strength and exact nature of the replacement property corresponds to selecting from a number of natural varieties of modal rings. The work generalises a result of Suszko who considered the S4 case.

Item Type: Journal Article
Murdoch Affiliation(s): School of Mathematical and Physical Sciences
Publisher: Springer
Copyright: © 2000 Birkhäuser Verlag Basel
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